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112 results on '"Riyasat, Mumtaz"'

5. Certain results for unified Apostol type-truncated exponential-Gould-Hopper polynomials and their relatives

Author

Araci, Serkan, Riyasat, Mumtaz, Nahid, Tabinda, and Khan, Subuhi

Subjects
Mathematics - General Mathematics, 11B68, 05A10, 11B65
Abstract

The present article aims to introduce a unified family of the Apostol type-truncated exponential-Gould-Hopper polynomials and to characterize its properties via generating functions. A unified presentation of the generating function for the Apostol type-truncated exponential-Gould-Hopper polynomials is established and its applications are given. By the use of operational techniques, the quasi-monomial properties for the unified family are proved. Several explicit representations and multiplication formulas related to these polynomials are obtained. Some general symmetric identities involving multiple power sums and Hurwitz-Lerch zeta functions are established by applying different analytical means on generating functions., Comment: 20 pages

Published
2020

9. Determinant approach to the 2-Iterated q-Appell and mixed type q-Appell polynomials

Author

Khan, Subuhi and Riyasat, Mumtaz

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In this article, the 2-iterated q-Appell family is introduced. Certain 2-iterated q-Appell and mixed type q-special polynomials are considered as members of this family. The numbers related to these polynomials are obtained. The determinant definitions for the 2-iterated q-Appell family and for the 2-iterated and mixed type q-Appell polynomials are established. The graphs of some 2-iterated q-Appell and mixed type q-Appell polynomials are drawn for different values of indices and the roots of these polynomials are also investigated for certain values of index n by using Matlab. Finally, the approximate solutions of the real zeros of these polynomials are given.

Published
2016

10. 2-iterated Sheffer polynomials

Author

Khan, Subuhi and Riyasat, Mumtaz

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a determinantal definition for these polynomials is established. The quasi-monomial and other properties of these polynomials are derived. The generating function, determinantal definition, quasi-monomial and other properties for some new members belonging to this family are also considered.

Published
2015

11. Symmetry identities for 2-variable Apostol type and related polynomials

Author

Khan, Subuhi, Riyasat, Mumtaz, and Yasmin, Ghazala

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In this article, certain symmetry identities for the 2-variable Apostol type polynomials are derived. By taking suitable values of parameters and indices, the symmetry identities for the special cases of the 2-variable Apostol type polynomials are established. Further, the symmetry identities for certain members belonging to the 2-variable Apostol type polynomials are also considered.

Published
2015

16. A Note on q-Bernoulli–Euler Polynomials

Author

Khan, Subuhi, Riyasat, Mumtaz, Kacprzyk, Janusz, Series editor, Pal, Nikhil R., Advisory editor, Bello Perez, Rafael, Advisory editor, Corchado, Emilio S., Advisory editor, Hagras, Hani, Advisory editor, Kóczy, László T., Advisory editor, Kreinovich, Vladik, Advisory editor, Lin, Chin-Teng, Advisory editor, Lu, Jie, Advisory editor, Melin, Patricia, Advisory editor, Nedjah, Nadia, Advisory editor, Nguyen, Ngoc Thanh, Advisory editor, Wang, Jun, Advisory editor, Panigrahi, Bijaya Ketan, editor, Hoda, M. N., editor, Sharma, Vinod, editor, and Goel, Shivendra, editor

Published
2018
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18. INTEGRAL TRANSFORMS AND EXTENDED HERMITE-APOSTOL TYPE FROBENIUS-GENOCCHI POLYNOMIALS.

Author

WANI, SHAHID AHMAD and RIYASAT, MUMTAZ

Subjects
POLYNOMIALS, INTEGRO-differential equations, SPECIAL functions, MATHEMATICAL physics, INTEGRAL transforms
Abstract

The schemata for applications of the integral transforms of mathematical physics to recurrence relations, differential, integral, integro-differential equations and in the theory of special functions has been developed. The article aims to introduce and present operational representations for a new class of extended Hermite-Apostol type Frobenius-Genocchi polynomials via integral transforms. The recurrence relations and some identities involving these polynomials are established. The article concludes by establishing a determinant form and quasi-monomial properties for the Hermite-Apostol type Frobenius-Genocchi polynomials and for their extended forms. [ABSTRACT FROM AUTHOR]

Published
2024
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22. Properties and Graphical Representations of the 2-Variable Form of the Simsek Polynomials

Author

Khan, Subuhi, Nahid, Tabinda, and Riyasat, Mumtaz

Abstract

This article is written with an objective to introduce the 2-variable Simsek polynomials Yn(x,y;λ,δ) and to investigate some properties of these polynomials. The 2-variable forms of Changhee and Daehee polynomials are also considered. Several important recurrence relations involving the Cauchy, Changhee, Daehee and Simsek numbers are derived. The hypergeometric function representation for an integral involving these polynomials is obtained. The graphical representations of the 2-variable Simsek polynomials are considered for suitable values of the index nand parameters λand δ. The article is concluded with the derivation of non-linear differential equation and related identity for the Simsek numbers.

Published
2024
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23. Hermite-based hybrid polynomials and some related properties

Author

Riyasat, Mumtaz, Khan, Subuhi, and Shah, Shakir

Abstract

In this paper, the two-variable one-parameter generalized Hermite-based hybrid polynomials are introduced by means of generating function, series definition and determinant definition. The recurrence relations, shift operators, differential, integro-differential and partial differential equations for these polynomials are established via factorization method. The two-variable one-parameter generalized Hermite-based Bernoulli, Euler and Genocchi polynomials are studied as the particular members and some examples are considered in terms of these polynomials to give the applications of main results. The graphical representation and interpretation is also shown for these polynomials.

Published
2024
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37. 𝑞-Tricomi functions and quantum algebra representations.

Author

Riyasat, Mumtaz, Nahid, Tabinda, and Khan, Subuhi

Subjects
*REPRESENTATIONS of algebras, *GROUP algebras, *QUANTUM groups, *GENERATING functions, *MATHEMATICIANS
Abstract

The quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of q-special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras. This paper focuses on introducing the q-Tricomi functions and 2D q-Tricomi functions through the generating function and series expansion and for the first time establishing a connecting relation between the q-Tricomi and q-Bessel functions. The behavior of these functions is described through shapes, and the contrast between them is observed using mathematical software. Further, the problem of framing the q-Tricomi and 2D q-Tricomi functions in the context of the irreducible representation (ω) of the two-dimensional quantum algebra ℰq(2) is addressed, and certain relations involving these functions are obtained. 2-Variable 1-parameter q-Tricomi functions and their relationship with the 2-variable 1-parameter q-Bessel functions are also explored. [ABSTRACT FROM AUTHOR]

Published
2021
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46. STUDY OF GENERALIZED LEGENDRE-APPELL POLYNOMIALS VIA FRACTIONAL OPERATORS.

Author

KHAN, SUBUHI, WANI, SHAHID AHMAD, and RIYASAT, MUMTAZ

Subjects
LEGENDRE'S functions, DIFFERENTIAL equations, POLYNOMIALS, FRACTIONAL calculus, FUNCTIONAL integration
Abstract

In this article, the operational definitions and integral representations are combined to introduce new families of the generalized Legendre and generalized Legendre-Appell polynomials. The explicit summation formulae, determinant definitions and recurrence relations for the generalized Legendre-Appell polynomials are derived by making use of the integral transforms and appropriate operational rules. An analogous study of these results for the generalized Legendre-Bernoulli, Legendre-Euler and Legendre-Genocchi polynomials is presented. Several identities for these polynomials are also derived by employing appropriate operational definitions. [ABSTRACT FROM AUTHOR]

Published
2020

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